Generation of Lognormal Synthetic Lyman-$α$ Forest Spectra for $P_{1D}$ Analysis

TL;DR

This work introduces a fast, flexible lognormal framework to generate one-dimensional Ly$\alpha$ forest spectra tailored for $P_{\mathrm{1D}}$ analyses in DESI. By directly solving for a redshift-dependent Gaussian correlation function $\xi_G$ to reproduce target flux statistics, the method avoids fixed input power forms and yields high-fidelity mocks across a wide range of redshift and scale. The approach achieves sub-percent agreement in mean flux evolution and percent-level accuracy in $P_{\mathrm{1D}}$ over the DESI EDR range, with robust convergence when generating large mock ensembles, enabling thorough validation of $P_{\mathrm{1D}}$ pipelines and systematic studies. Extensions to include astrophysical contaminants, continuum uncertainties, and instrumental effects are discussed, positioning the mocks for end-to-end validation and precision cosmology with Ly$\alpha$ data in DESI and future surveys.

Abstract

The one-dimensional flux power spectrum (P1D) of the Lyman-$α$ forest probes small-scale structure in the intergalactic medium (IGM) and is therefore sensitive to a variety of cosmological and astrophysical parameters. These include the amplitude and shape of the matter power spectrum, the thermal history of the IGM, the sum of neutrino masses, and potential small-scale fluctuations due to the nature of dark matter. However, P1D is also highly sensitive to observational and instrumental systematics, making accurate synthetic spectra essential for validating analyses and quantifying these effects, especially in high-volume surveys like the Dark Energy Spectroscopic Instrument (DESI). We present an efficient lognormal mock framework for generating one-dimensional Lyman-$α$ forest spectra tailored for P1D analysis. Our method captures the redshift evolution of the mean transmitted flux and the scale-dependent shape and amplitude of the one-dimensional flux power spectrum by tuning Gaussian field correlations and transformation parameters. Across the DESI Early Data Release (EDR) redshift range ($2.0 \leq z \leq 3.8$), and a wide range of scales ($10^{-4}$ s km$^{-1} \leq k \leq 1.0$ s km$^{-1}$), our mocks recover the mean flux evolution with redshift to sub-percent accuracy, and the P1D at the percent level. Additionally, we discuss potential extensions of this framework, such as the incorporation of astrophysical contaminants, continuum uncertainties, and instrumental effects. Such improvements would expand its utility in ongoing and upcoming surveys and enable a broader range of validation efforts and systematics studies for P1D inference and precision cosmology.

Figures (5)

• Figure 1: An example line-of-sight realization at redshift z = 3.6, illustrating the impact of varying an individual parameter value during mock generation. The value of the variance, $\sigma_F^2$, is shown spanning a $\pm75\%$ range around the best-fit (fiducial) value given in Table \ref{['table.2']}. Each row, from top to bottom, shows a key step in the transformation pipeline: the Gaussian random field, the redshifted baryon fluctuation approximation $\delta_b(z)$, the optical depth $\tau(z)$, and the final transmitted flux $F(z)$.
• Figure 2: Comparison of the $P_{\mathrm{1D}}$ of mocks generated using the method presented in this work with the DESI EDR measurement and the previous mock generation method. DESI EDR (blue, solid line) is a fit of eq. \ref{['eq.7']} to the $P_{\mathrm{1D}}$ measurement by Karaçaylı et al. (2024) Karacayli_2024. This Work (orange, dotted) shows the $P_{\mathrm{1D}}$ produced with our method, which agrees with the DESI EDR fit within 1%. The previous method by Karaçaylı et al. (2020) Karacayli_2020 (black, dashed) is also shown. The four panels are redshifts $z = 2, 3, 4,$ and $5$.
• Figure 3: Comparison of the analytic model for the mean flux from mocks generated in this work to a model fit to observational data. (Top) Comparison between the default mean flux redshift evolution model fit by Turner et al. (2024)turner24 to DESI DR1 (blue) and the best-fit analytic model of this work, using the derived parameter values in Table \ref{['table.2']} (orange, dotted) over the redshift range $2 \lesssim z \lesssim 5$. (Bottom) Percent difference between the DESI mean flux measurement and the our analytic prediction.
• Figure 4: A demonstration of how well mocks generated using our method recover the input power spectrum target model. (Top) Comparison of the default $P_{\mathrm{1D}}$ model, given by eq. \ref{['eq.7']} fit to the DESI EDR $P_{\mathrm{1D}}$ measurement Karacayli_2024 (blue, dashed), with the binned $P_{\mathrm{1D}}$ measurement averaged over 1000 line-of-sight realizations per redshift (orange). This comparison is done for select redshifts $z = 2.0, 2.6$, $3.2$, and $3.8$, which spans the range of the DESI EDR measurement. (Bottom) Percent difference between the average measured power from our mocks and the input target model.
• Figure 5: A demonstration of how well our mocks recover the input mean flux model. (Top) Average mean flux measured from a set of 1000 independent line-of-sight mock realizations at each target redshift in the range $2.0 \leq z \leq 3.8$ (orange, dotted) compared to the measurement by Turner et al., (2024) turner24 (blue) on DESI DR1. This DESI measurement was the target model used to tune the fitting parameters for mock generation in § \ref{['Section: fitting_mean_flux']}. (Bottom) Percent difference between the DESI DR1 mean flux measurement turner24 and the average mean flux measured from our mocks.